A method for spectroscopically analyzing a sample by detecting a radiation field change as a function of the radiation power density in the sample



Apnl 22, 1969 R. H. BAUHAUS ET AL 3,440,529

METHOD FOR SPECTROSCOPICALLY ANALYZING A SAMPLE BY DETECTING A RADIATION FIELD CHANGE AS A FUNCTION OF THE RADIATION POWER DENSITY IN THE SAMPLE Filed Feb. 21, 1966 Sheet of 2 ELECTROMAGNETIC RADIATION FIELD VERSUS I POWER DENSITY WITH SAMPLE IN AND SAMPLE 2 OUT OF FIELD D O 111 5 2 E FIELD WITH 0 62 SAMPLE OUT .0: II] I U FIELD WITH SAMPLE IN 2 I: 9 I- A [I I AFIELD MAX. PROPORTIONAL TO 1 O z 2 I 9 LU 0 I2 I II 6E I 60. 0 10 LIJ 2 Lu J O I I U PROPORTIONAL T0 P,

POWER DENSITY, 1, OF THE ELECTROMAGNETIC RADIATION IN THE SAMPLE Figure I 'LO- -C "7 PARTIAL PRESSURE "7 I Pg KO IS p O If PURE SAMPLE ADDEDPI- IMPURITIES ADDED-- TA PRE URE MICRONS OF MERCURY To L 88 INVENTORS HOWAR D C. POULTER HOWARD w HARRINGTON RATIO OF uNsATuRATED INTENSITY COEFFICIENTS, RICHARD H BAUHAUS P/J- 77PARTIAL PRESSURE 0 AND RATIO OF MAXIMUM SIGNALS, BY h Q C- M 77 I VERSUS TOTAL PRESSURE ATTORNEY FIgure 2 April 22, 1969 BAUHAUS ET AL 3,440,529

METHOD FOR SPECTROSCOPICALLY ANALYZING A SAMPLE BY DETECTING A RADIATION FIELD CHANGE AS A FUNCTION OF THE RADIATION POWER DENSITY IN THE SAMPLE Filed Feb. 21, 1966 Sheet 2 of 2 MODULATOR SOURCE SAMPLE DETECTOR REFERENCE isure 3 INVENTORS HOWARD C POULTER HOWARD W. HARRINGTON RICHARD H. BAUHAUS BY QLQ- 3mm ATTORNEY United States Patent 3,440,529 A METHOD FOR SPECTROSCOPICALLY ANALYZ- ING A SAMPLE BY DETECTING A RADIATION FIELD CHANGE AS A FUNCTION OF THE RA- DIATION POWER DENSITY IN THE SAMPLE Richard H. Bauhaus, Howard W. Harrington, and Howard C. Poulter, Palo Alto, Calif., assignors to Hewlett- Packard Company, Palo Alto, Calif., a corporation of California Filed Feb. 21, 1966, Ser. No. 528,854 Int. Cl. GOlr 27/04 US. Cl. 324-585 9 Claims ABSTRACT OF THE DISCLOSURE Electromagnetic radiation is applied to a sample of matter to produce a spectroscopic transition that causes a change in each field component of the applied electromagnetic radiation. The change in each field component is varied by varying the power density of the electromagnetic radiation applied to the sample. Variations in the change of a selected field component are detected as a function of the variations in power density under power saturated conditions to determine the maximum change of the selected field component.

This invention relates to a method for analyzing a sample of matter of the type in which a spectroscopic transition may be produced by the interaction of electromagnetic radiation with the sample.

In the past such methods have been generally concerned with detecting the electromagnetic radiation frequency at which a selected spectroscopic transition occurs in the sample and the electromagnetic radiation power change associated with the'selected spectroscopic transition. However, it is an object of this invention to provide a method which is concerned with detecting the electromagnetic radiation field change associated with a selected spectro scopic transition in the sample as a function of the electromagnetic radiation density in the sample for the purpose of determining the maximum electromagnetic radiation field change.

It is another object of this invention to provide a method for improving the acquisition and interpretation of certain spectroscopy data already available and for making possible the acquisition of additional spectroscopy data.

Other and incidental objects of this invention will become apparent from a reading of this specification and an inspection of the accompanying drawing in which:

FIGURE 1 is a plot for either the electric field component or the magnetic field component showing the electromagnetic radiation field change associated with a selected spectroscopic transition produced by interaction of the electromagnetic radiation with the sample to be analyzed as a function of the power density in the sample of the electromagnetic radiation interacting with the samp FIGURE 2 is a plot comparing the unsaturated intensity coefiicient and the maximum side band field, which is proportional to the maximum change in the microwave electric field as a function of pressure where pressure is first increased by adding pure sample and then further increased by adding impurities; and

FIGURE 3 is a block diagram of apparatus for implementing the method of this invention.

In general this method comprises as one step applying electromagnetic radiation to the sample of matter to be analyzed for interacting the eletcromagnetic radiation with the sample to produce a selected spectroscopic transition in the sample. A change, A in the field components of the electromagnetic radiation interacting with the sample is associated with the spectroscopic transition as Shown in FIGURE 1 by the spacing between curve 10, which corresponds to interaction between the applied electromagnetic radiation and the sample, and curve 12, which corresponds to the absence of sample in the field of the applied electromagnetic radiation. This electromagnetic radiation field change, A varies with the power density in the sample of the electromagnetic radiation interacting with the sample as further shown in FIG- URE l. A maximum electric field change, Afleld MAX., will be observed if the amount of electromagnetic radiation energy change caused by interaction with the sample to produce the spectroscopic transition approaches a constant value as the electromagnetic radiation power density in the sample is increased, in other words if power saturation occurs. Thus, as another step by detecting the change, A in the electromagnetic radiation interacting with the sample while varying the electromagnetic radiation power density in the sample the maximum electromagnetic radiation field change, Afield MAX., may be determined either by direct measurement or by extrapolation. As shown below this maximum electromagnetic radiation field change, Afield MAX., has useful properties which, for example, make it and the electromagnetic radiation power density required to produce it useful for examining dipole moments, rotational energy transfer, relaxation processes and other molecular properties.

Some of the useful properties of the electromagnetic radiation field change, Afield MAX., may be illustrated in the specific context of the gas-phase pure rotational spectroscopic transitions observed with a Stark-modulated microwave spectrometer, since these spectroscopic transitions readily power saturate. For a Stark-modulated microwave spectrometer tuned to an absorption frequency of the gas-phase sample and using a conventional Stark cell the microwave power is attenuated according to the Beers-Lamberts relationship,

In Equation 1 P is the power after the incident power, P has passed a distance of L through the sample with an absorption or intensity coefficient Since P =E 1Z where Z is the impedance and E the incident microwave electric field, Equation 1 can be rewritten as In Equation 2 the approximation is made that 'yL l so that only the first term in the expansion of the exponential in Equation 1 need be considered. The microwave electric field at the detector can be written, neglecting higher order side bands, as

where w is the angular frequency of the absorption and t is the time. The amplitude factor of the co side bands is given as Because of power saturation, the intensity coefiicient 'y becomes It can be assumed with no loss of generality that the microwave electric field is uniformly distributed in the sample. Combining Equations 4 and 5 yields A: EO'YOL 21r(1l-KE The maximum value of A as a function of E is found by setting the first derivative of A with respect to E equal to zero. It is thusly found that A has a maximum value when Combination of Equations 6 and 7 gives MAX. 7 471- where A is the maximum side band field amplitude and is directly proportional to the observed signal in a Starkmodulated microwave spectrometer operated in accordance with the principles of this invention. To evaluate the properties of 1 the expressions for 7 and K must be substituted into Equation 8. The unsaturated intensity coefficient 7 can be written as 9 161r FN 'Yo=m IMnI where:

The quantity K is given as h=Planks constant and t=meantime between equilibrium restoring collisions (i.e.

relaxation time).

Combining Equations 8, 9, and 10 yields the desired equation,

Since the maximum side band field '17 is directly proportional to the maximum electromagnetic radiation field change, Afleld MAX., the useful properties of Afleld MAX. can be illustrated by comparing the properties of 1 with the properties of the unsaturated intensity coefficient, 7 This may be done by comparing Equations 11 and 9 and by assuming that 7:! or that -r/t is a constant. Thus, it is seen that the maximum side band field amplitude 1; is proportional to FN, the number of molecules of the absorbing specie, whereas the unsaturated intensity coeflicient 7 is proportion to FNT. Since for a pressure broadened absorption 1- is proportion to 1/N a further comparison of maximum side band field amplitude 9 and the unsaturated intensity coefiicient 'y can be easily accomplished by examining both 1 and 70 as a function of pressure where the total pressure is the sum of the partial pressures of the absorbing specie and impurities. As shown by the curve 14 in FIGURE 2 the intensity coefiicient 7 is independent of a change in the pressure of pure sample, but decreases with increasing pressure when nonabsorbing material, that is, impurities are added to the sample. The maximum side band field amplitude 1;, however, varies linearly with pressure for the pure sample and is independent of the concentration of the non-absorbing material, or impurities, as shown by the curve 16 in FIGURE 2. Thus, under any pressure conditions the maximum side band field amplitude '27 gives a measure of the number of the absorbing specie, whereas the intensity coeflicient 70 does not.

The rate of change of the maximum side band field amplitude n with temperature can also be utilized to gain information about the molecular distribution functions.

By inspection of Equations 11 and 9 one can see that the temperature coefiicient of the maximum side band field amplitude n depends on the variation of F with temperature, since 7/ t has been assumed equal to one, whereas the temperature coefiicient of the intensity coefiicient 'y additionally depends on the variation of 'T' with temperature. The rate of change of P,,, the power required to measure the maximum side band field amplitude 1;, as a function of temperature also gives information on the temperature dependence of molecular relaxation processes since P depends on [p and 1 because P, is equal to where A is the free space wavelength and A is the waveguide wavelength.

Measuring the maximum sideband field amplitude 1 provides maximum signal and thus maximum sensitivity. On the other hand the unsaturated intensity coefiicient 'y must be measured at low power levels because of power saturation. This means less signal and thus lower sensitivity.

While the above description has assumed a uniform power density throughout the sample this need not necessarily be the case. The maximum sideband field amplitude 1 and the power required to measure it, P,,, for the non-uniform spacial power density case are each related to the uniform power density distribution case by a constant which depends only on the power density distribution. Therefore, the properties of the maximum sideband field amplitude 17, and the power required to measure it, P, for the nonuniform power density distribution case are the same as those described above.

The method of this invention may be implemented in the microwave region of the electromagnetic radiation spectrum with apparatus such as that shown in the copending patent application Ser. No. 342,487 of Nicholas J. Kuhn filed on Feb. 4, 1964, issued as US. Patent No. 3,317,827 on May 2, 1967, and assigned to Hewlett- Packard Company (the same assignee as the present invention). However, this method may also be implemented for substantially the entire electromagnetic radiation spectrum indicated by the more general apparatus shown in block form in FIGURE 3. A source 18 applies electromagnetic radiation to a sample containing means 20 for interacting the electromagnetic radiation with the sample to produce a selected spectroscopic transition for which there is a corresponding change, A in the field components of the interacting electromagnetic radiation. The electromagnetic radiation power density in the sample is altered, for example, by changing the amount of electromagnetic radiation applied by the source 18 to the sample. A detector 22 is coupled to the sample containing means 20 for detecting the electromagnetic radiation field change, Afield, to determine the maximum field change, Afleld MAX. In order to increase the sensitivity of the system comprising blocks 18-22, a modulator 24 may be coupled to either the source 18, the sample containing means 20, or the detector 22 for applying a timevarying signal thereto to produce a time variation of the field changes, A A reference arm 26 may also be connected across the sample Containing means 20 as shown in FIGURE 3 for the purpose of optimizing the performance of detector 22 independent of the power level in the sample.

We claim:

1. A method for analyzing a sample of matter of the type in which a spectroscopic transition may be produced by the interaction of electromagnetic radiation with the sample at the frequency of the spectroscopic transition, said method comprising the steps of:

applying electromagnetic radiation including electric and magnetic field components to the sample for interacting with the sample at a selected frequency to produce a spectroscopic transition causing a c0rresponding change in each field component of the electromagnetic radiation interacting with the samp varying the power density of the electromagnetic radiation interacting with the sample at the selected frequency to vary the change in each field component of the electromagnetic radiation interacting with the sample; and

detecting variations in the change of a selected field component of the electromagnetic radiation interacting with the sample at the selected frequency with variations in the power density of the electromagnetic radiation interacting with the sample for determining the maximum change of the selected field component.

2. The method of claim 1:

including the additional step of time-varying the change in the selected field component; and wherein the detecting step comprises detecting the variation with time of the change in the selected field component for different power densities of the electromagnetic radiation interacting with the sample at the selected frequency. 3. The method of claim 1: including the additional step of time-varying the interaction of the electromagnetic radiation with the sample for producing a sideband field; and

wherein the detecting step comprises detecting the amplitude of the sideband field for dilferent power densities of the electromagnetic radiation interacting with the sample at the selected frequency.

4. A method for analyzing a sample of matter in which a spectroscopic transition may be produced by the interaction of electromagnetic radiation with the sample at the frequency of the spectroscopic transition, said method comprising the steps of:

applying electromagnetic radiation including electric and magnetic field components to the sample to be analyzed, said radiation interacting with the sample at a selected frequency to produce a spectroscopic transition causing a corresponding change in each field component of the electromagnetic radiation interacting with the sample;

varying the power density of the electromagnetic radiation interacting with the sample at the selected frequency to vary the change in a selected field component of the electromagnetic radiation interacting with the sample along a curve relating the change in the selected field component to the power density of the electromagnetic radiation interacting with the sample; and

detecting the change in the selected field component for at least two different radiation power densities in the sample, at least one of these power densities being above the power saturation threshold of the sample, so as to obtain spectroscopic transition data at a determinable position along this curve.

5. A method as in claim 4 wherein the sample has a broadening time T, a relaxation time t, and a molecular concentration N and wherein the ratio of the broadening time 1 to the relaxation time tis held constant so that the spectroscopic transition data obtained is a linear function of the molecular concentration N and independent of the broadening time -r and the relaxation time t.

6',-A method as in claim 4 wherein the sample has a broadening time 1-, a relaxation time t, and a molecular concentration N and wherein the molecular concentration N is held constant so that the spectroscopic transition data obtained is a measure of the ratio of the broadening time 1- to the relaxation time t.

7. A method as in claim 4:

including the additional step of time-varying the change in the selected field component; and

wherein the detecting step comprises detecting the variation with time of the change in the selected field component for at least two different power densities References Cited UNITED STATES PATENTS 5/1953 Hershberger 32458.5 5/1957 Hershberger 32458.5

RUDOLPH V. ROLINEC, Primary Examiner.

P. F. WILLE, Assistant Examiner.

U.S. DEPARTMENT OF COMMERCE PATENT OFFICE Washington, D.C. 20231 UNITED STATES PATENT OFFICE CERTIFICATE OF CORRECTION Patent No. 3,440,529 April 22, 1969 Richard H. Bauhaus et a1.

It is certified that error appears in the above identified patent and that said Letters Patent are hereby corrected as shown below:

Column 3, lines 33 to 35, after equation (10) insert where: line 45, after "field" insert amplitude line 55, "proportion" should read proportional line 56, "proportion" should read proportional Column 4 lines ll 14, in the equation, "K should read K Signed and sealed this 14th day of April 1970.

(SEAL) Attest:

Edward M. Fletcher, Jr. WILLIAM E. SCHUYLER, JR Attesting Officer Commissioner of Patents 

